Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

JGWeissman comments on Bayesian Utility: Representing Preference by Probability Measures - Less Wrong

10 Post author: Vladimir_Nesov 27 July 2009 02:28PM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (35)

You are viewing a single comment's thread. Show more comments above.

Comment author: JGWeissman 27 July 2009 11:41:56PM 0 points [-]

As I already explained, that only works for actions that exclude some outcomes and renormalize the probabilities of remaining outcomes, preserving the ratios of their probabilities.

Suppose O had 2 elements, x1 and x2, such that p(x1) = p(x2) = .5. If you take action A, then you have conditional probabilities p(x1|A) = .2 and p(x2|A) = .8. In this case, your transformation of P(x|A) = P(x, A)/P(A) does not work. Because A did not remove x1 as a possibility, it just made it less likely.

Comment author: Vladimir_Nesov 27 July 2009 11:58:10PM *  0 points [-]

P(x|A) = P(x,A)/P(A) is by definition of conditional probability. You are trying to interpret x1 and x2 as events, while in grandparent comment x are elements of the sample space. If you want to consider non-concrete outcomes, compose them from smaller elements. For example, you can have P(O1)=P(O2)=.5, P(O1|A)=.2, P(O2|A)=.8, if O1={x1,x2}, O2={x3,x4}, A={x1,x3}, and p(x1)=.1, p(x2)=.4, p(x3)=.4, p(x4)=.1.